Confidence Intervals: Values of
from an x distribution. The sample mean is 100.
(a) Suppose the x distribution has
(b) Suppose the x distribution has
(c) Suppose the x distribution has
(d) Compare the margins of error for pans (a) through (c). As the standard deviation decreases, does the margin of error decrease?
(e)Critical Thinking Compare the lengths of the confidence intervals for pans (a) through (c). As the standard deviation decreases, does the length of a 90% confidence interval decrease?
(a)
To find: A 90% confidence interval for
Also, find the margin of error.
Answer to Problem 20P
Solution:
The 90% confidence interval for
Explanation of Solution
Calculation:
Given that x distribution with sample mean
We have to find 90% confidence interval,
90% confidence interval is
The 90% confidence interval for
Margin of error is
(b)
To find: A 90% confidence interval for
Also, find the margin of error.
Answer to Problem 20P
Solution:
The 90% confidence interval for
Explanation of Solution
Calculation:
Given that x distribution with sample mean
We have to find 90% confidence interval,
90% confidence interval is
The 90% confidence interval for
Margin of error is
(c)
To find: A 90% confidence interval for
Also, find the margin of error.
Answer to Problem 20P
Solution:
The 90% confidence interval for
Explanation of Solution
Calculation:
Given that x distribution with sample mean
We have to find 90% confidence interval,
90% confidence interval is
The 90% confidence interval for
Margin of error is
(d)
The comparison of the margins of error for parts (a) through (c) and determines whether the margin of error decrease as the standard deviation decreases.
Answer to Problem 20P
Solution:
Yes, the margin of error also decreases as the standard deviation decreases.
Explanation of Solution
For
For
For
As standard deviation decreases, the margin of error also decreases.
(e)
The comparison of confidence interval for part (a) through (c). Also determine whether the length of confidence interval decreases, as the standard deviation decreases.
Answer to Problem 20P
Solution:
Yes, the length of confidence interval also decreases, as the standard deviation decreases.
Explanation of Solution
For
For
For
As the standard deviation decreases, the length of confidence interval also decreases.
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Chapter 8 Solutions
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